Corrector estimates for a thermo-diffusion model with weak thermal coupling
- Muntean, Adrian
- Reichelt, Sina
2010 Mathematics Subject Classification
- 35B27 35Q79 74A15 78A48
- Homogenization, corrector estimates, periodic unfolding, gradient folding operator, perforated domain, thermo-diffusion, composite media
The present work deals with the derivation of corrector estimates for the two-scale homogenization of a thermo-diffusion model with weak thermal coupling posed in a heterogeneous medium endowed with periodically arranged high-contrast microstructures. The terminology ``weak thermal coupling'' refers here to the variable scaling in terms of the small homogenization parameter ε of the heat conduction-diffusion interaction terms, while the ``high-contrast'' is thought particularly in terms of the heat conduction properties of the composite material. As main target, we justify the first-order terms of the multiscale asymptotic expansions in the presence of coupled fluxes, induced by the joint contribution of Sorret and Dufour-like effects. The contrasting heat conduction combined with cross coupling lead to the main mathematical difficulty in the system. Our approach relies on the method of periodic unfolding combined with ε-independent estimates for the thermal and concentration fields and for their coupled fluxes
- Multiscale Model. Simul., 16 (2018), pp. 807--832, DOI 10.1137/16M109538X .